1.file "nextafterf.s" 2 3 4// Copyright (c) 2000 - 2004, Intel Corporation 5// All rights reserved. 6// 7// 8// Redistribution and use in source and binary forms, with or without 9// modification, are permitted provided that the following conditions are 10// met: 11// 12// * Redistributions of source code must retain the above copyright 13// notice, this list of conditions and the following disclaimer. 14// 15// * Redistributions in binary form must reproduce the above copyright 16// notice, this list of conditions and the following disclaimer in the 17// documentation and/or other materials provided with the distribution. 18// 19// * The name of Intel Corporation may not be used to endorse or promote 20// products derived from this software without specific prior written 21// permission. 22 23// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 24// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 25// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 26// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS 27// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 28// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 29// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 30// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY 31// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING 32// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 33// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 34// 35// Intel Corporation is the author of this code, and requests that all 36// problem reports or change requests be submitted to it directly at 37// http://www.intel.com/software/products/opensource/libraries/num.htm. 38// 39// History 40//============================================================== 41// 02/02/00 Initial version 42// 03/03/00 Modified to conform to C9X, and improve speed of main path 43// 03/14/00 Fixed case where x is a power of 2, and x > y, improved speed 44// 04/04/00 Unwind support added 45// 05/12/00 Fixed erroneous denormal flag setting for exponent change cases 1,3 46// 08/15/00 Bundle added after call to __libm_error_support to properly 47// set [the previously overwritten] GR_Parameter_RESULT. 48// 09/09/00 Updated fcmp so that qnans do not raise invalid 49// 12/15/00 Corrected behavior when both args are zero to conform to C99, and 50// fixed flag settings for several cases 51// 05/20/02 Cleaned up namespace and sf0 syntax 52// 02/10/03 Reordered header: .section, .global, .proc, .align 53// 12/14/04 Added error handling on underflow. 54// 55// API 56//============================================================== 57// float nextafterf( float x, float y ); 58// input floating point f8, f9 59// output floating point f8 60// 61// Registers used 62//============================================================== 63GR_max_pexp = r14 64GR_min_pexp = r15 65GR_exp = r16 66GR_sig = r17 67GR_lnorm_sig = r18 68GR_sign_mask = r19 69GR_exp_mask = r20 70GR_sden_sig = r21 71GR_new_sig = r22 72GR_new_exp = r23 73GR_lden_sig = r24 74GR_snorm_sig = r25 75GR_exp1 = r26 76GR_x_exp = r27 77GR_min_den_rexp = r28 78// r36-39 parameters for libm_error_support 79 80GR_SAVE_B0 = r34 81GR_SAVE_GP = r35 82GR_SAVE_PFS = r32 83 84GR_Parameter_X = r36 85GR_Parameter_Y = r37 86GR_Parameter_RESULT = r38 87GR_Parameter_TAG = r39 88 89FR_lnorm_sig = f10 90FR_lnorm_exp = f11 91FR_lnorm = f12 92FR_sden_sig = f13 93FR_sden_exp = f14 94FR_sden = f15 95FR_save_f8 = f33 96FR_new_exp = f34 97FR_new_sig = f35 98FR_lden_sig = f36 99FR_snorm_sig = f37 100FR_exp1 = f38 101FR_tmp = f39 102 103// 104// Overview of operation 105//============================================================== 106// nextafterf determines the next representable value 107// after x in the direction of y. 108 109 110.section .text 111GLOBAL_LIBM_ENTRY(nextafterf) 112 113// Extract signexp from x 114// Form smallest denormal significand = ulp size 115{ .mlx 116 getf.exp GR_exp = f8 117 movl GR_sden_sig = 0x0000010000000000 118} 119// Form largest normal exponent 120// Is x < y ? p10 if yes, p11 if no 121// Form smallest normal exponent 122{ .mfi 123 addl GR_max_pexp = 0x1007e, r0 124 fcmp.lt.s1 p10,p11 = f8, f9 125 addl GR_min_pexp = 0x0ff81, r0 ;; 126} 127 128// Is x=y? 129{ .mfi 130 getf.sig GR_sig = f8 131 fcmp.eq.s0 p6,p0 = f8, f9 132 nop.i 0 133} 134// Extract significand from x 135// Form largest normal significand 136{ .mlx 137 nop.m 0 138 movl GR_lnorm_sig = 0xffffff0000000000 ;; 139} 140 141// Move largest normal significand to fp reg for special cases 142{ .mfi 143 setf.sig FR_lnorm_sig = GR_lnorm_sig 144 nop.f 0 145 addl GR_sign_mask = 0x20000, r0 ;; 146} 147 148// Move smallest denormal significand and signexp to fp regs 149// Is x=nan? 150// Set p12 and p13 based on whether significand increases or decreases 151// It increases (p12 set) if x<y and x>=0 or if x>y and x<0 152// It decreases (p13 set) if x<y and x<0 or if x>y and x>=0 153{ .mfi 154 setf.sig FR_sden_sig = GR_sden_sig 155 fclass.m p8,p0 = f8, 0xc3 156(p10) cmp.lt p12,p13 = GR_exp, GR_sign_mask 157} 158{ .mfi 159 setf.exp FR_sden_exp = GR_min_pexp 160 nop.f 999 161(p11) cmp.ge p12,p13 = GR_exp, GR_sign_mask ;; 162} 163 164.pred.rel "mutex",p12,p13 165 166// Form expected new significand, adding or subtracting 1 ulp increment 167// If x=y set result to y 168// Form smallest normal significand and largest denormal significand 169{ .mfi 170(p12) add GR_new_sig = GR_sig, GR_sden_sig 171(p6) fmerge.s f8=f9,f9 172 dep.z GR_snorm_sig = 1,63,1 // 0x8000000000000000 173} 174{ .mlx 175(p13) sub GR_new_sig = GR_sig, GR_sden_sig 176 movl GR_lden_sig = 0x7fffff0000000000 ;; 177} 178 179// Move expected result significand and signexp to fp regs 180// Is y=nan? 181// Form new exponent in case result exponent needs incrementing or decrementing 182{ .mfi 183 setf.exp FR_new_exp = GR_exp 184 fclass.m p9,p0 = f9, 0xc3 185(p12) add GR_exp1 = 1, GR_exp 186} 187{ .mib 188 setf.sig FR_new_sig = GR_new_sig 189(p13) add GR_exp1 = -1, GR_exp 190(p6) br.ret.spnt b0 ;; // Exit if x=y 191} 192 193// Move largest normal signexp to fp reg for special cases 194// Is x=zero? 195{ .mfi 196 setf.exp FR_lnorm_exp = GR_max_pexp 197 fclass.m p7,p0 = f8, 0x7 198 nop.i 999 199} 200{ .mfb 201 nop.m 999 202(p8) fma.s0 f8 = f8,f1,f9 203(p8) br.ret.spnt b0 ;; // Exit if x=nan 204} 205 206// Move exp+-1 and smallest normal significand to fp regs for special cases 207// Is x=inf? 208{ .mfi 209 setf.exp FR_exp1 = GR_exp1 210 fclass.m p6,p0 = f8, 0x23 211 addl GR_exp_mask = 0x1ffff, r0 212} 213{ .mfb 214 setf.sig FR_snorm_sig = GR_snorm_sig 215(p9) fma.s0 f8 = f8,f1,f9 216(p9) br.ret.spnt b0 ;; // Exit if y=nan 217} 218 219// Move largest denormal significand to fp regs for special cases 220// Save x 221{ .mfb 222 setf.sig FR_lden_sig = GR_lden_sig 223 mov FR_save_f8 = f8 224(p7) br.cond.spnt NEXT_ZERO ;; // Exit if x=0 225} 226 227// Mask off the sign to get x_exp 228{ .mfb 229 and GR_x_exp = GR_exp_mask, GR_exp 230 nop.f 999 231(p6) br.cond.spnt NEXT_INF ;; // Exit if x=inf 232} 233 234// Check 6 special cases when significand rolls over: 235// 1 sig size incr, x_sig=max_sig, x_exp < max_exp 236// Set p6, result is sig=min_sig, exp++ 237// 2 sig size incr, x_sig=max_sig, x_exp >= max_exp 238// Set p7, result is inf, signal overflow 239// 3 sig size decr, x_sig=min_sig, x_exp > min_exp 240// Set p8, result is sig=max_sig, exp-- 241// 4 sig size decr, x_sig=min_sig, x_exp = min_exp 242// Set p9, result is sig=max_den_sig, exp same, signal underflow and inexact 243// 5 sig size decr, x_sig=min_den_sig, x_exp = min_exp 244// Set p10, result is zero, sign of x, signal underflow and inexact 245// 6 sig size decr, x_sig=min_sig, x_exp < min_exp 246// Set p14, result is zero, sign of x, signal underflow and inexact 247// 248// Form exponent of smallest float denormal (if normalized register format) 249{ .mmi 250 adds GR_min_den_rexp = -23, GR_min_pexp 251(p12) cmp.eq.unc p6,p0 = GR_new_sig, r0 252(p13) cmp.eq.unc p8,p10 = GR_new_sig, GR_lden_sig ;; 253} 254 255{ .mmi 256(p6) cmp.lt.unc p6,p7 = GR_x_exp, GR_max_pexp 257(p8) cmp.gt.unc p8,p9 = GR_x_exp, GR_min_pexp 258(p10) cmp.eq.unc p10,p0 = GR_new_sig, r0 ;; 259} 260 261// Create small normal in case need to generate underflow flag 262{ .mfi 263(p10) cmp.le.unc p10,p0 = GR_x_exp, GR_min_pexp 264 fmerge.se FR_tmp = FR_sden_exp, FR_lnorm_sig 265(p9) cmp.gt.unc p9,p14 = GR_x_exp, GR_min_den_rexp 266} 267// Branch if cases 1, 2, 3 268{ .bbb 269(p6) br.cond.spnt NEXT_EXPUP 270(p7) br.cond.spnt NEXT_OVERFLOW 271(p8) br.cond.spnt NEXT_EXPDOWN ;; 272} 273 274// Branch if cases 4, 5, 6 275{ .bbb 276(p9) br.cond.spnt NEXT_NORM_TO_DENORM 277(p10) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO 278(p14) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO ;; 279} 280 281// Here if no special cases 282// Set p6 if result will be a denormal, so can force underflow flag 283// Case 1: x_exp=min_exp, x_sig=unnormalized 284// Case 2: x_exp<min_exp 285{ .mfi 286 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp 287 fmerge.se f8 = FR_new_exp, FR_new_sig 288 nop.i 999 ;; 289} 290 291{ .mfi 292 nop.m 999 293 nop.f 999 294(p7) tbit.z p6,p0 = GR_new_sig, 63 ;; 295} 296 297NEXT_COMMON_FINISH: 298// Force underflow and inexact if denormal result 299{ .mfi 300 nop.m 999 301(p6) fma.s.s0 FR_tmp = FR_tmp,FR_tmp,f0 302 nop.i 999 303} 304{ .mfb 305 nop.m 999 306 fnorm.s.s0 f8 = f8 // Final normalization to result precision 307(p6) br.cond.spnt NEXT_UNDERFLOW ;; 308} 309 310{ .mfb 311 nop.m 999 312 nop.f 999 313 br.ret.sptk b0;; 314} 315 316//Special cases 317NEXT_EXPUP: 318{ .mfb 319 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp 320 fmerge.se f8 = FR_exp1, FR_snorm_sig 321 br.cond.sptk NEXT_COMMON_FINISH ;; 322} 323 324NEXT_EXPDOWN: 325{ .mfb 326 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp 327 fmerge.se f8 = FR_exp1, FR_lnorm_sig 328 br.cond.sptk NEXT_COMMON_FINISH ;; 329} 330 331NEXT_NORM_TO_DENORM: 332{ .mfi 333 nop.m 999 334 fmerge.se f8 = FR_new_exp, FR_lden_sig 335 nop.i 999 336} 337// Force underflow and inexact 338{ .mfb 339 nop.m 999 340 fma.s.s0 FR_tmp = FR_tmp,FR_tmp,f0 341 br.cond.sptk NEXT_UNDERFLOW ;; 342} 343 344NEXT_UNDERFLOW_TO_ZERO: 345{ .mfb 346 cmp.eq p6,p0 = r0,r0 347 fmerge.s f8 = FR_save_f8,f0 348 br.cond.sptk NEXT_COMMON_FINISH ;; 349} 350 351NEXT_INF: 352// Here if f8 is +- infinity 353// INF 354// if f8 is +inf, no matter what y is return largest float 355// if f8 is -inf, no matter what y is return -largest float 356 357{ .mfi 358 nop.m 999 359 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig 360 nop.i 999 ;; 361} 362 363{ .mfb 364 nop.m 999 365 fmerge.s f8 = f8,FR_lnorm 366 br.ret.sptk b0 ;; 367} 368 369NEXT_ZERO: 370 371// Here if f8 is +- zero 372// ZERO 373// if f8 is zero and y is +, return + smallest float denormal 374// if f8 is zero and y is -, return - smallest float denormal 375 376{ .mfi 377 nop.m 999 378 fmerge.se FR_sden = FR_sden_exp,FR_sden_sig 379 nop.i 999 ;; 380} 381 382// Create small normal to generate underflow flag 383{ .mfi 384 nop.m 999 385 fmerge.se FR_tmp = FR_sden_exp, FR_lnorm_sig 386 nop.i 999 ;; 387} 388 389// Add correct sign from direction arg 390{ .mfi 391 nop.m 999 392 fmerge.s f8 = f9,FR_sden 393 nop.i 999 ;; 394} 395 396// Force underflow and inexact flags 397{ .mfb 398 nop.m 999 399 fma.s.s0 FR_tmp = FR_tmp,FR_tmp,f0 400 br.cond.sptk NEXT_UNDERFLOW ;; 401} 402 403NEXT_UNDERFLOW: 404// Here if result is a denorm, or input is finite and result is zero 405// Call error support to report possible range error 406{ .mib 407 alloc r32=ar.pfs,2,2,4,0 408 mov GR_Parameter_TAG = 269 // Error code 409 br.cond.sptk __libm_error_region // Branch to error call 410} 411;; 412 413NEXT_OVERFLOW: 414// Here if input is finite, but result will be infinite 415// Use frcpa to generate infinity of correct sign 416// Call error support to report possible range error 417{ .mfi 418 alloc r32=ar.pfs,2,2,4,0 419 frcpa.s1 f8,p6 = FR_save_f8, f0 420 nop.i 999 ;; 421} 422 423// Create largest double 424{ .mfi 425 nop.m 999 426 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig 427 nop.i 999 ;; 428} 429 430// Force overflow and inexact flags to be set 431{ .mfb 432 mov GR_Parameter_TAG = 155 // Error code 433 fma.s.s0 FR_tmp = FR_lnorm,FR_lnorm,f0 434 br.cond.sptk __libm_error_region // Branch to error call 435} 436;; 437 438GLOBAL_LIBM_END(nextafterf) 439libm_alias_float_other (nextafter, nextafter) 440 441 442LOCAL_LIBM_ENTRY(__libm_error_region) 443.prologue 444 445// (1) 446{ .mfi 447 add GR_Parameter_Y=-32,sp // Parameter 2 value 448 nop.f 0 449.save ar.pfs,GR_SAVE_PFS 450 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs 451} 452{ .mfi 453.fframe 64 454 add sp=-64,sp // Create new stack 455 nop.f 0 456 mov GR_SAVE_GP=gp // Save gp 457};; 458 459 460// (2) 461{ .mmi 462 stfs [GR_Parameter_Y] = f9,16 // STORE Parameter 2 on stack 463 add GR_Parameter_X = 16,sp // Parameter 1 address 464.save b0, GR_SAVE_B0 465 mov GR_SAVE_B0=b0 // Save b0 466};; 467 468.body 469// (3) 470{ .mib 471 stfs [GR_Parameter_X] = FR_save_f8 // STORE Parameter 1 on stack 472 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address 473 nop.b 0 474} 475{ .mib 476 stfs [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack 477 add GR_Parameter_Y = -16,GR_Parameter_Y 478 br.call.sptk b0=__libm_error_support# // Call error handling function 479};; 480{ .mmi 481 nop.m 0 482 nop.m 0 483 add GR_Parameter_RESULT = 48,sp 484};; 485 486// (4) 487{ .mmi 488 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack 489.restore sp 490 add sp = 64,sp // Restore stack pointer 491 mov b0 = GR_SAVE_B0 // Restore return address 492};; 493{ .mib 494 mov gp = GR_SAVE_GP // Restore gp 495 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs 496 br.ret.sptk b0 // Return 497};; 498 499LOCAL_LIBM_END(__libm_error_region) 500 501 502.type __libm_error_support#,@function 503.global __libm_error_support# 504